Exact trigonometric values

Table of contents 12° 15°
18° 21° 24° 27° 30°
33° 36° 39° 42° 45°
48° 51° 54° 57° 60°
63° 66° 69° 72° 75°
78° 81° 84° 87° 90°

0° and 90°




Other values


90°




Other values


45°

Derivation (Graph)

45° 45° 1 1 x

Derivation (Half-Angle Formula)




45°




Other values


30° and 60°

Derivation (Graph)

30° 60° 60° 1 1 2 2 x

30°




Other values


60°




Other values


15° and 75°

Derivation (Graph)

1 y 15° 2 2 x 30° 15°


Derivation (Half-Angle Formula)





15°




Other values


75°




Other values


18°, 36°, 54°, and 72°

Derivation (Graph)

x 36° 1 72° 1 x x y 18°




18°




Other values


36°




Other values


54°




Other values


72°




Other values


9°, 27°, 63°, and 81°

Derivation (Half-Angle Formula)









Other values


27°




Other values


63°




Other values


81°




Other values


6°, 12°, 24°, 42°, 48°, 66°, 78°, and 84°

Derivation (Sum and Difference Formula)








Other values


12°




Other values


24°




Other values


42°




Other values


48°




Other values


66°




Other values


78°




Other values


84°




Other values


3°, 21°, 33°, 39°, 51°, 57°, 69°, and 87°

Derivation (Sum and Difference Formula)








Other values


21°




Other values


33°




Other values


39°




Other values


51°




Other values


57°




Other values


69°




Other values


87°




Other values